Frotbactor and method of using same



. v 1,628266 May 10, 1927. G. M. NAVA PROTRACTOR AND METHOD OF USING SAME Filed June 11 1926 INVENTOR GEN/12o N l/ 7 Patented May 10, 1927.

UNITED STATES e-E ARoM. NAVA, on NEW YORK, N. Y.

.Pnorm c'ron AND METHOD or USING SAME.

Application filed June 11,

This invention relates to improvements in protractors and the method of using the same, and has particular reference to a protractor for use in the construction of musical instruments. i

It is well known that in the so-called musical octave there are six full tones or twelve half tones and that the proportion of the fundamental tone to the next higher reproduction thereof is as 1:2. Heretofore, in the construction of musical instruments, such as guitars, banjos and the like, wherein frets are employed ithas not been possible to accurately determine the relative distance between the frets 0n the instruments in order to obtain what is known as the equal temperament. As now constructed, such instruments are capable of sounding only full and half tones and the distances between the frets, which vary in accordance with the tones to be produced, are not calculated to an accurate and precise degree. a

An object of the present invention is to accurately obtain the proper proportionate parts of the length of a. string of an instrument necessary for the production of different tones constituting an octave and to thereby determine the distances between the various frets.

Another object is to provide a protractor by means of which it is possible to. obtain, within the compass of the so-called octave, not only full and half tones, of which latter there are twelve, but also twenty-four quartor tones, forty-eighteighth tones, ninetysix sixteenth tones, and so on.

The above and other objects will appear more clearly from the following detail description, when taken in connection with the accompanying drawing,- which illustrates a preferred embodiment of the inventive idea.

In the drawing- Figure 1 is a plan view of the protractor; and

Figures 2 to 5 are diagrammatic views illustrating, progressively, the various steps in the use of the protractor.

For purposes of the present invention the divisions of the protractor 1, which may be semi-circular and made of transparent material, are based upon a circle having 576 divisions of which 288 divisions are includedin the protractor. The are of the protractor is divided into three equal segments 2, 3 and 4, each including 96 divisions. The segments 2 and 4; are on either side of the central seg- ,three equal segments. the protractor a number of points are 1926. Serial No. 115,152.

use ofthis rotr'actor, be divided into half, quarter, e1 g 1th and sixteenth tones.

Toaccomplish the aforesaid result, a line 6 (Figure 2) is first drawn, which is equal -in length to the eflective length of a string of a guitar, banjo or the like.

This line is then representative of the fundamental tone and a line 7 'bisecting the line 6 divides said tone into two octaves according to the known theory. As shown in Figure 3', the 'protractor is then placed at one extremity of the line 6 with the line 8 marked upon the protractor aligned with said line 6. From the geometric center 9 of the markings in the segments 2 and 4 of the protractor representing 96 divisions, the.

projected to intersect the 1 (points 11. With the distance belines 10 are then line .7 at

tween sai center 9 and either of the points as a radius a circle 12 (Figures l and 5) is described and this circle is then bisected dicular to the line 6. The semi-circle thus formedis divided by the two lines 10 into marked on the arc of said circle on opposite sides of the line 6 equal to the number of tones to be reproduced at intervals by the string of the instrument within the scope V, of the octave. Thus,as shown in Figure 5, between the points. 0 and96 on each side of the line 6, five points have been marked which divide each segment of the circle into six equal parts each of which represents a full tone Should half tones be desired, then each of said six parts is equally subdivided by the use of the protractor and for quarter tones, etc., the sub-divisions may again'be divided in a manner which will be apparent from the foregoing description. The corresponding points on opposite sides of the line 6 are now connected by chords which intersect said line at the points 13 to 17, thus dividing the portion of the line between one end and the point of intersechen by the use of lieu thereof with the line 7 into six sections (each representing a full tone) with the distances between said points gradually decreasing toward the end 18 of the line. Vith the line 6 thus divided the distance between any one of the points 1?) to 17 (or additional points, should the line be divided tel-halt tones, quarter tones, etc.) and the end 18 of the line represents accurately the proportionate part of the length of the string of an instrument necessary for a perfect pro duction of a particular tone in the octave and it is at such points that a 'lret tor a stringed instrument. is placed on the neck thereof.

It will be obvious that the points 13 to 17 on the line 6 may be ascertained in practically the same manner as above described by employing a quadrantal protractor instead of a semi-circular one. In other words, a protractor which is a duplicate of either half of the protractor shown in Figure 1 may be utilized in securing the desired result. Thus with the line 8 defining one of the right angular edges of the protractor and the segment 2 marked exactly as shown, said edge may be aligned with the line 6 and a single line 10 then projected from the point 9 to intersect the line 7 at a point 11 in the same manner as previously described[ The circle 12 is then made and intersected by the line drawn through the point 9 perpendicular to the line 6. In accordance with the divisions in the segment 2 a number of points are marked on the arc of the circle 12, as previously described, whereupon by the use of one of the right angular edges of the protraetor chords are projected from said points perpendicular to and intersecting the line 6 at points 13 to 17, thus securing the proper divisions of said line.

IVhat is claimed is:

1. A protractor for use in determining the relative positions between the frets of stringed instruments, including a semi-circular body having means thereon defining a central segment and other segn'ients arranged on opposite sides of said central segments, respectively, said other segments being divided by radial lines into at least six equal parts. a.

2. A. protractor for use in determining the relative positions between the frets ol stringed instruments, including a semi-circular body havinglines thereon defining a central segment and other segments arranged on opposite sides of said central segment, respectively. each or? said segments including one third of the total arc of said body and only said other segments being provided with circumferential division marks.

3. A protractor for use in determining the relative positions between the frets of stringed instrui'nents, including a sen1i-circular bod l'iaving means thereon defining central ginent and other segments arranged on opposite sides of said central segment, each of said segments including one-third of the total. are of said body and only said other segments being provided with circumferential division marks which divide each segment into at least six equal parts.

l. The herein described method which consists in bisectinginto sections with one line a second line representative of a fundamental tone and equal in length to the effective length of a string of a stringed instrument, interseiting the first named line with a third line extended from one extremity of the second named line at a predeter mined angle thereto, describing an are about said extremity of said second line with a radius equal to the distance between said extremity and the point of intersection of said third line with said first named line so that the latter line will be intersected by said are, intersecting said arc by a fourth line extending through said extremity perpendicular to said second line, marking a por tion of said are between said second and fourth named lines with at least six equal divisions, and intersecting one section of said second line with chords proj cted from said division markings in parallel relation to said fourth line to determine on said second line the proportionate lengths thereof necessary for the production of different tones constituting an octave.

In testimony whereof I have allixed my signature.

GENARO M. NLVA. 

